Freezing rain on limbs does not cause direct biological problems for trees. The ice can in fact insulate the limbs from deeper cold rather than causing any deeper freezing. Ice accumulation on limbs is a threat only if it adds significantly to the weight on those limbs and results in breakage.
All trees have different mechanical properties that can either make them resistant to ice damage or readily cause breakage. Birch, for instance, has real elastic qualities to its wood that allows it to bend with the extra weight of ice a certain degree before there is breakage. Norway Maples which have a “harder” wood than Birch, actually has a brittle quality that more readily breaks when it is bent even a little. Oaks have the best quality of strength and elasticity.
In general a light glazing of ice is of no consequence. More than a quarter inch of ice starts to cause light damage to vulnerable tree species. More than a 1/2 inch of ice can cause widespread limb damage. As ice accumulation approaches an inch, the extra weight can even topple defective trees.
If you are concerned about your trees, contact your Cohen & Master arborist for an inspection.